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Question 289802: sketch a polynomial that has even-degree with one relative maximum and two relative minima
Answer by jsmallt9(3759)   (Show Source):
You can put this solution on YOUR website! - The degree of a polynomial is the highest exponent in the polynomial.
- The term with the highest exponent will dominate the polynomial for large positive and negative values of x. The highest power term will overwhelm the others for large values of x, no matter what the other terms are!
- Your polynomial has an even degree. Since even powers of x are positive, even if x is negative, and since this term dominates, the polynomial will have large positive values for large values of x (positive or negative).
- On a graph large positive values of x are far to the right and large negative values of x are far to the left.
- Large positive values for y are up high.
- Since the polynomial, the y, will have large positive values for large positive and negative values of x, the graph will be up high far to the right and far to the left.
- In between we want two relative minima and one relative maximum.
Putting all this together we should arrive at a graph that looks like a curvy "W": High on each end with two relative minima and one relative maximum. (Do not draw the "W" with straight lines! There are no "straight" parts and no corners in the graph of a polynomial of degree higher than 1.)
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